Which expression is a factor of \( x^{2}-2 x-24 \)

To factor the expression \( x^2 - 2x - 24 \), we need to find two numbers that multiply to \(-24\) (the constant term) and add up to \(-2\) (the coefficient of the linear term). Those numbers are \( 4 \) and \(-6\). Thus, we can rewrite the expression as: \[ (x - 6)(x + 4) \] This means that \( (x - 6) \) and \( (x + 4) \) are factors of the original quadratic. Another fun fact: factoring quadratics is like solving a puzzle! You're looking for two pieces that fit perfectly together to recreate the original expression, and when you find those numbers, it feels like a little victory—like finding buried treasure! Additionally, if you're working on similar problems, always remember to check your factors by multiplying them back out to ensure they give you the original equation. It's a great way to avoid simple mistakes, like confusing signs or miscalculating products! Try it out with other quadratic expressions to sharpen your factoring skills!